Control of Hopf Bifurcation in a Fluid-Flow  Model in Wireless Networks

Abstract

Abstract:

Abstract： Aimed at the Hopf bifurcation problem of a fluid-flow model for the congestion control in wireless networks, comparative experiments of three kinds of control method were conducted in this paper. By choosing the communication delay as a bifurcation parameter, it was proved that with three kinds of the controller, the critical value of bifurcation were changed and the stable region were enlarged, and the Hopf bifurcation of the system was delayed. Numerical results verified that the performance of the Hopf bifurcation with delay feedback controller, the performance of the hybrid controller and the performance of the state feedback controller in a wireless network were different; the state feedback controller can most effectively control Hopf bifurcation of the system, followed by the hybrid controller.

Key words: wireless networks, congestion control, Hopf bifurcation, delay feedback, hybrid control, state feedback

CLC Number:

XU Chao1,2,ZHOU Yunlong2,WANG Yang2. Control of Hopf Bifurcation in a Fluid-Flow Model in Wireless Networks[J]. Journal of Shanghai Jiaotong University, 2014, 48(10): 1479-1484.

References

［1］Liu F, Wang H O, Guan Z H. Stability analysis and control of bifurcation in a TCP fluid flow model of wireless networks ［C］∥Proceedings of the 10th World Congress on Intelligent Control and Automation. Beijing: IEEE, 2012: 10261030. ［2］Dong T, Liao X F, Huang T W. Dynamics of a congestion control model in a wireless access network ［J］. Nonlinear Analysis: Real World Applications, 2013, 14(1): 671683.

［3］侯萍, 王执铨. 无线网络拥塞控制中流体流模型的Hopf分岔及其稳定性［J］. 电子与信息学报, 2010, 32(4): 983987.

HOU Ping, WANG Zhiquan. Stability and Hopf bifurcation of a fluidflow model for congestion control in wireless networks［J］. Journal of Electronics and Information, 2010, 32(4): 983987.

［4］Ding D W, Zhu J, Luo X S, et al. Controlling Hopf bifurcation in fluid flow model of internet congestion control system ［J］. International Journal of Bifurcation and Chaos, 2009, 19(4): 14151424.

［5］Li N, Yuan H Q, Sun H Y, et al. Adaptive control of bifurcation and chaos in a timedelayed system ［J］. Chinese Phys, 2013, 22(3): 030508.

［6］Guo S T, Feng G, Liao X F, et al. Hopf bifurcation control in a congestion control model via dynamic delayed feedback ［J］. AIP Chaos, 2008, 18(4): 31043117.

［7］Xiao M, Zheng W X. Bifurcation control of a congestion control model via state feedback ［J］. International Journal of Bifurcation and Chaos, 2013, 23(6): 1330018.

［8］Liu Z G, Chung K W. Hybrid control of bifurcation in continuous nonlinear dynamical systems ［J］. International Journal of Bifurcation and Chaos, 2005, 15(12): 38953903.

［9］Luo X S, Chen G R, Wang B H, et al. Hybrid control of perioddoubling bifurcation and chaos in discrete nonlinear dynamical systems ［J］. Chaos, Solitons and Fractals, 2003, 18(4): 775783.

［10］Liu F, Wang H O, Guan Z H. Hopf bifurcation control in the XCP for the Internet congestion control system ［J］. Nonlinear Analysis: Real World Applications, 2012, 13(3): 14661479.

［11］Zhao H Y, Wen X. Hopf bifurcation for a smallworld network model with parameters delay feedback control ［J］. Nonlinear Dyn, 2011, 63(3): 345357.

［12］Hassard B D, Kazarinoff N D, Wan Y H. Theory and applications of Hopf bifurcation ［M］. Cambridge UK: Cambridge Univ Press, 1981.

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Control of Hopf Bifurcation in a Fluid-Flow Model in Wireless Networks

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